Transition from Quasiperiodicity to Chaos for Three Coaxial Vortex Rings

DOI10.1002/zamm.20000801344zbMath0963.76017OpenAlexW1988359811MaRDI QIDQ4498950

Omar M. Knio, F. Blackmore

Publication date: 30 January 2001

Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/zamm.20000801344

zbMATH Keywords

KAM theoryideal fluidchaotic motionsMelnikov theoryperiodic motionsHamilton's equationsquasiperiodic motionsmean radius of ringsPoincaré-Birkhoff theorythree coaxial vortex rings

Mathematics Subject Classification ID

Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Vortex flows for incompressible inviscid fluids (76B47)

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Cites Work

• Quasi-periodic motions of vortex systems
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• KAM theory analysis of the dynamics of three coaxial vortex rings
• Existence of KAM tori in the phase-space of lattice vortex systems
• Hamiltonian description of axisymmetric vortex flows and the system of vortex rings
• The dynamics of three vortices revisited
• Motion of a Curved Vortex Filament with Decaying Vortical Core and Axial Velocity
• Nonintegrability of two problems in vortex dynamics
• SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS